A heavy-duty truck tire contains a fixed mass of air at an initial absolute pressure of 2.… — JAMB UTME

A heavy-duty truck tire contains a fixed mass of air at an initial absolute pressure of $2.00 \times 10^5\text{ Pa}$ and a temperature of $27^\circ\text{C}$ . After traveling a long distance, friction causes the temperature of the air inside the tire to increase to $57^\circ\text{C}$ while its volume remains constant. What is the new absolute pressure of the air inside the tire in pascals ( $\text{Pa}$ )?

Answer: 220000 Pa

Answer

The new absolute pressure of the air inside the tire is

220,000\text{ Pa}

(or

2.20 \times 10^5\text{ Pa}

According to Gay-Lussac's Law, at constant volume, pressure is directly proportional to absolute temperature (

P \propto T

). Converting temperatures to Kelvin gives

T_1 = 300\text{ K}

and

T_2 = 330\text{ K}

. Calculating

P_2 = P_1 \times \frac{T_2}{T_1}

gives

2.00 \times 10^5\text{ Pa} \times \frac{330}{300} = 220,000\text{ Pa}

Step-by-Step Solution

Convert the initial and final temperatures from Celsius to the absolute Kelvin scale.

T_1 = 27^\circ\text{C} + 273 = 300\text{ K}

and

T_2 = 57^\circ\text{C} + 273 = 330\text{ K}

All gas law equations require absolute temperatures in Kelvin.

Apply the Pressure Law (Gay-Lussac's Law) for a fixed volume of gas.

\frac{P_1}{T_1} = \frac{P_2}{T_2}

When volume is constant, gas pressure is directly proportional to absolute temperature.

Substitute the known values into the equation to calculate the final pressure

P_2

P_2 = 2.00 \times 10^5\text{ Pa} \times \frac{330\text{ K}}{300\text{ K}} = 2.20 \times 10^5\text{ Pa} = 220,000\text{ Pa}

Multiplying the initial pressure by the ratio of absolute temperatures gives the new pressure.

Key Concept

Pressure Law (Gay-Lussac's Law)

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